Prove the sets A and B defined below are equal.
A = {(a, b) is a member of Z+ × Z+|a is a factor of b}
B is defined recursively by
Initial Step: (1, 1) is a member of B
Recursive Step: If (a, b) is a member of B and c is a member of Z+ then
(ac, bc) is a member of B and (a, bc) is a member of B